scholarly journals Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2509
Author(s):  
Ibrahim Ayuba ◽  
Lateef T. Akanji ◽  
Jefferson L. Gomes ◽  
Gabriel K. Falade

This paper reports an analytical study conducted to investigate the behaviour of tracers undergoing creeping flow between two parallel plates in porous media. A new coupled model for the characterisation of fluid flow and transport of tracers at pore scale is formulated. Precisely, a weak-form solution of radial transport of tracers under convection–diffusion-dominated flow is established using hypergeometric functions. The velocity field associated with the radial transport is informed by the solution of the Stokes equations. Channel thickness as a function of velocities, maximum Reynolds number of each thickness as a function of maximum velocities and concentration profile for different drift and dispersion coefficients are computed and analysed. Analysis of the simulation results reveals that the dispersion coefficient appears to be a significant factor controlling the concentration distribution of the tracer at pore scale. Further analysis shows that the drift coefficient appears to influence tracer concentration distribution but only after a prolonged period. This indicates that even at pore scale, tracer drift characteristics can provide useful information about the flow and transport properties of individual pores in porous media.

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
Soroush Aramideh ◽  
Pavlos P. Vlachos ◽  
Arezoo M. Ardekani

2017 ◽  
Vol 9 (3) ◽  
pp. 596-620 ◽  
Author(s):  
Peiqi Huang ◽  
Jinru Chen ◽  
Mingchao Cai

AbstractIn this work, we study numerical methods for a coupled fluid-porous media flow model. The model consists of Stokes equations and Darcy's equations in two neighboring subdomains, coupling together through certain interface conditions. The weak form for the coupled model is of saddle point type. A mortar finite element method is proposed to approximate the weak form of the coupled problem. In our method, nonconforming Crouzeix-Raviart elements are applied in the fluid subdomain and the lowest order Raviart-Thomas elements are applied in the porous media subdomain; Meshes in different subdomains are allowed to be nonmatching on the common interface; Interface conditions are weakly imposed via adding constraint in the definition of the finite element space. The well-posedness of the discrete problem and the optimal error estimate for the proposed method are established. Numerical experiments are also given to confirm the theoretical results.


2016 ◽  
Vol 18 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Safa Sabet ◽  
Moghtada Mobedi ◽  
Turkuler Ozgumus

Abstract In the present study, the fluid flow in a periodic, non-isotropic dual scale porous media consisting of permeable square rods in inline arrangement is analyzed to determine permeability, numerically. The continuity and Navier-Stokes equations are solved to obtain the velocity and pressure distributions in the unit structures of the dual scale porous media for flows within Darcy region. Based on the obtained results, the intrinsic inter and intraparticle permeabilities and the bulk permeability tensor of the dual scale porous media are obtained for different values of inter and intraparticle porosities. The study is performed for interparticle porosities between 0.4 and 0.75 and for intraparticle porosities from 0.2 to 0.8. A correlation based on Kozeny-Carman relationship in terms of inter and intraparticle porosities and permeabilities is proposed to determine the bulk permeability tensor of the dual scale porous media.


Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-24 ◽  
Author(s):  
Rebecca Allen ◽  
Shuyu Sun

We compute effective properties (i.e., permeability, hydraulic tortuosity, and diffusive tortuosity) of three different digital porous media samples, including in-line array of uniform shapes, staggered-array of squares, and randomly distributed squares. The permeability and hydraulic tortuosity are computed by solving a set of rescaled Stokes equations obtained by homogenization, and the diffusive tortuosity is computed by solving a homogenization problem given for the effective diffusion coefficient that is inversely related to diffusive tortuosity. We find that hydraulic and diffusive tortuosity can be quantitatively different by up to a factor of ten in the same pore geometry, which indicates that these tortuosity terms cannot be used interchangeably. We also find that when a pore geometry is characterized by an anisotropic permeability, the diffusive tortuosity (and correspondingly the effective diffusion coefficient) can also be anisotropic. This finding has important implications for reservoir-scale modeling of flow and transport, as it is more realistic to account for the anisotropy ofboththe permeability and the effective diffusion coefficient.


Author(s):  
John Ll. Moses

To supplement viscosity measurements of water made by the more conventional methods, for example by capillary or rotating cylinder viscometers, it was decided to make a ‘radial flow viscometer’ as outlined by H. Gümbel in Barr's ‘Monograph of viscosity’ (1)†. The radial flow viscometer consists principally of two flat discs separated by a known distance, the fluid being forced to flow radially inward and leaving the discs through a hole in the centre of one of the discs. Before the method could be adopted, it was essential to devise a formula which would account for the inertia term in the equation of motion, since disregard of the inertia term would render the final equation inaccurate. An equation has been developed from the Navier-Stokes equations, which gives a solution involving elliptic integrals. An attempt is made to compare the above solution with the well-known creeping flow solution and with experimental results. Preliminary tests for varying flows and varying widths of separation of the discs have shown discrepancies of under 2 per cent between experimental and theoretical values.


1996 ◽  
Vol 19 (3) ◽  
pp. 163-180 ◽  
Author(s):  
M. Rashidi ◽  
L. Peurrung ◽  
A.F.B. Tompson ◽  
T.J. Kulp

Volume 4 ◽  
2004 ◽  
Author(s):  
Michael J. Oliver ◽  
Jaikrishnan R. Kadambi ◽  
Beverly Saylor ◽  
Martin Ferer ◽  
Grant S. Bromhal ◽  
...  

The study of flow and transport in porous media has relevance in many industrial, environmental (Geologic sequestration of CO2) and biological disciplines. In many engineering applications we require the knowledge of the velocity field for flow through porous objects. Historically, simplified models such as Darcy’s law [1,2], provide a reasonable description of the flow in the interior for single phase flow but require empirical coefficients to match the boundary conditions with the outer flow. The scientific basis for understanding flow and transport phenomena in porous media has largely been developed from experimental and theoretical studies in “bulk” or macroscopic systems in which coupled behavior at the pore scale is not measured or observed directly. To understand the flow behavior at the pore scale, flow characterization in porous media is very important. Multiphase, immiscible, low Re flow through a simulated porous media is studied experimentally. The experimental test cell, Figure 1, designed in collaboration with the Department of Energy, National Energy Technology Laboratory (DOE NETL), was manufactured from an optically clear polycarbonate material. It has a lattice type pattern of 2.5 mm pores bodies interconnected by angular capillary throats varying in size from 200 μm to 1000 μm. The experimental flow loop (Figure 2), utilizes air as the displacing fluid and sodium iodide (NaI) solution in water as the defending fluid. Air is provided at a constant pressure at the inlet. The refractive indices of the NaI solution and the optically clear test cell are matched to facilitate the observance of the air-liquid interface motion. Experimental data recorded with respect to time are the inlet gage pressure, delta pressure, inlet to outlet, across the test cell, volume flow rate at the outlet and the position of the displacement interface as the invading fluid, air, displaces the defending fluid, NaI solution. Parameters that can be varied in the experiment are viscosity ratio, micro and macro capillary number, the bond number and the volume flow rate. The details of the test loop are provided in Figure 2. The figure shows the piping arrangement to fill the test cell with the NaI solution and supplying the air for the tests. A CCD camera (Redlake ES 1.0 cross-correlation camera; resolution: 1008 × 1018 pixels) equipped with a 20 mm Micro Nikkor lens (Nikon) and a data acquisition system consisting of a PC and a PIXCI D2X frame grabber card (EPIX) is utilized to obtain a series of digital images as the invading air enters the test cell through the inlet manifold and makes way through the liquid until the breakthrough to the exit manifold. The pore scale velocity of the displacement interface is determined using a “Difference Threshold Technique” developed at Case Western Reserve University (CWRU), Laser Flow Diagnostics Lab (LFDL), Department of Mechanical and Aerospace Engineering. The difference threshold technique developed to processing the images is described in the next section.


Author(s):  
Paul SAPIN ◽  
Paul Duru ◽  
Florian Fichot ◽  
Marc Prat ◽  
Michel Quintard

2017 ◽  
Author(s):  
Pu He ◽  
Li Chen ◽  
Yu-Tong Mu ◽  
Wen-Quan Tao

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